An auto-adhesion model for MEMS surfaces taking into account the effect of surface roughness

Although a lot of work has been done on understanding auto-adhesion (stiction) in MEMS, the effect of surface roughness has never been extensively addressed. In this paper, a model is presented, which describes the auto-adhesion interaction energy of micromachined surfaces in contact. Included in the model is the capillary force, in such a way that it can be readily extended to accommodate electrostatic and van der Waals forces as well, in combination with the roughness of the contacting surfaces. By investigating the effect of the height distribution of the surfaces, a term is derived for the surface interaction energy in different environmental conditions as a function of the mean separation between the rough surfaces. To obtain an equilibrium distance between the surfaces, the repulsive part of the interaction is also modeled. The combination of these terms gives us the equilibrium distance between the surfaces and the corresponding surface interaction energy, thereby quantifying the effect environmental conditions have on auto-adhesion. The results of the model agree well with surface interaction energies in MEMS known from literature for different environmental conditions.